# Self-Reference in Large Language Models: The Introspection Threshold for Recursive Self-Improvement

arXiv: https://arxiv.org/abs/2607.04277 · HTML: https://mlsanity.com/paper/2607.04277/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Self-rewarding alignment and self-training, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 46 of its 80 references that are in the map.
- First posted on arXiv 5 Jul 2026.

## Placed in

- Synthetic data and self-improvement for LLMs / [Self-rewarding alignment and self-training](https://mlsanity.com/synth/self-rewarding-alignment-and-self-training/)

## Builds on (most cited first, 30 of 46)

- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [LLM Evaluators Recognize and Favor Their Own Generations](https://mlsanity.com/paper/2404.13076/) (2024)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [Darwin Godel Machine: Open-Ended Evolution of Self-Improving Agents](https://mlsanity.com/paper/2505.22954/) (2025)
- [SkillRL: Evolving Agents via Recursive Skill-Augmented Reinforcement Learning](https://mlsanity.com/paper/2602.08234/) (2026)
- [The Parallelism Tradeoff: Limitations of Log-Precision Transformers](https://mlsanity.com/paper/2207.00729/) (2022)
- [A Comprehensive Survey of Self-Evolving AI Agents: A New Paradigm Bridging Foundation Models and Lifelong Agentic Systems](https://mlsanity.com/paper/2508.07407/) (2025)
- [A Survey of Self-Evolving Agents: What, When, How, and Where to Evolve on the Path to Artificial Super Intelligence](https://mlsanity.com/paper/2507.21046/) (2025)
- [Recursive Introspection: Teaching Language Model Agents How to Self-Improve](https://mlsanity.com/paper/2407.18219/) (2024)
- [Self-Taught Optimizer (STOP): Recursively Self-Improving Code Generation](https://mlsanity.com/paper/2310.02304/) (2023)
- [Do I Know This Entity? Knowledge Awareness and Hallucinations in Language Models](https://mlsanity.com/paper/2411.14257/) (2024)
- [Looking Inward: Language Models Can Learn About Themselves by Introspection](https://mlsanity.com/paper/2410.13787/) (2024)
- [Consciousness in Artificial Intelligence: Insights from the Science of Consciousness](https://mlsanity.com/paper/2308.08708/) (2023)
- [A Survey on Self-Evolution of Large Language Models](https://mlsanity.com/paper/2404.14387/) (2024)
- [Tell me about yourself: LLMs are aware of their learned behaviors](https://mlsanity.com/paper/2501.11120/) (2025)
- [Me, Myself, and AI: The Situational Awareness Dataset (SAD) for LLMs](https://mlsanity.com/paper/2407.04694/) (2024)
- [Model Collapse Demystified: The Case of Regression](https://mlsanity.com/paper/2402.07712/) (2024)
- [Emergent Introspective Awareness in Large Language Models](https://mlsanity.com/paper/2601.01828/) (2026)
- [Reasoning Beyond Language: A Comprehensive Survey on Latent Chain-of-Thought Reasoning](https://mlsanity.com/paper/2505.16782/) (2025)
- [Language Models Are Capable of Metacognitive Monitoring and Control of Their Internal Activations](https://mlsanity.com/paper/2505.13763/) (2025)
- [Long Term Memory: The Foundation of AI Self-Evolution](https://mlsanity.com/paper/2410.15665/) (2024)

## Built on by (most cited first, 2 of 2)

- [MetaRSI / RSI2: A Meta-Recursive Self-Improving System for Recursive Self-Improving Systems Themselves](https://mlsanity.com/paper/2609.06396/) (2026)
- [Dalek: A Constructive Agent Machine](https://mlsanity.com/paper/2609.03546/) (2026)

## Abstract (arXiv)

The pursuit of self-evolving AI raises a critical question: when is autonomous self-improvement sustainable rather than degenerative? Drawing an analogy to von Neumann's complexity threshold for self-reproducing automata, we argue that sustainable recursive self-improvement in Large Language Models (LLMs) requires a functional analogue: introspection -- the system's capacity to simulate its own operations and target modifications. Grounded in Kleene's Second Recursion Theorem, we demonstrate the theoretical existence of such introspective programs. However, an empirical review reveals that while current LLMs exhibit quasi-introspection (e.g., partial metacognition), they fall short of true introspection due to structural bottlenecks: a lack of complete self-access, the feedforward nature of the Transformer, and computational class constraints that prevent fixed-point iteration. We conclude by outlining architectural paths to cross this complexity threshold and discussing the associated safety implications.